Theorem 1.1 [1]}
Let \(L\in (0, \infty )\)  and \(\mu \in [0, \infty )\)  and \(f\in \mathcal {F}_{\mu ,L}(\mathbb {R}^n)\) . For any \(x,y\in \mathbb {R}^n\) , we have

\(\tfrac{1}{2(1-\tfrac{\mu }{L})}\left(\tfrac{1}{L}\left\Vert \nabla f(x)-\nabla f(y)\right\Vert ^2+\mu \left\Vert x-y\right\Vert ^2-\tfrac{2\mu }{L}\left\langle \nabla f(y)-\nabla f(x),y-x\right\rangle \right)\le f(x)-f(y)-\left\langle \nabla f(y), x-y\right\rangle .\) 
